Understanding the Sources of Error in MBAR through Asymptotic Analysis

Multiple sampling strategies commonly used in molecular dynamics, such as umbrella sampling and alchemical free energy methods, involve sampling from multiple thermodynamic states. Commonly, the data are then recombined to construct estimates of free energies and ensemble averages using the Multistate Bennett Acceptance Ratio (MBAR) formalism. However, the error of the MBAR estimator is not well-understood: previous error analysis of MBAR assumed independent samples and did not permit attributing contributions to the total error to individual thermodynamic states. In this work, we derive a novel central limit theorem for MBAR estimates. This central limit theorem yields an error estimator which can be decomposed into contributions from the individual Markov chains used to sample the states. We demonstrate the error estimator for an umbrella sampling calculation of the alanine dipeptide in two dimensions and an alchemical calculation of the hydration free energy of methane. In both cases, the states' individual contributions to the error provide insight into the sources of error of the simulations. Our numerical results demonstrate that the time required for the Markov chain to decorrelate in individual thermodynamic states contributes considerably to the total MBAR error. Moreover, they indicate that it may be possible to use the contributions to tune the sampling and improve the accuracy of MBAR calculations.Comment: 13 pages, 4 figur

Does White Clover (Trifolium repens) Abundance in Temperate Pastures Determine Sitona obsoletus (Coleoptera: Curculionidae) Larval Populations?

To determine if host plant abundance determined the size of clover root weevil (CRW) Sitona obsoletus larval populations, a study was conducted over four years in plots sown in ryegrass (Lolium perenne) (cv. Nui) sown at either 6 or 30 kg/ha and white clover (Trifolium repens) sown at a uniform rate of 8 kg/ha. This provided a range of % white clover content to investigate CRW population establishment and impacts on white clover survival. Larval sampling was carried out in spring (October) when larval densities are near their spring peak at Lincoln (Canterbury, New Zealand) with % clover measured in autumn (April) and spring (September) of each year. Overall, mean larval densities measured in spring 2012, 2013, 2014 and 2015 were 310, 38, 59 and 31 larvae m-2, respectively. There was a significant decline in larval populations between 2012 and 2013, but spring populations were relatively uniform thereafter. The mean % white clover measured in autumns of 2012 to 2015 was 17, 10, 3 and 11%, respectively. In comparison, mean spring % white clover from 2012 to 2015, averaged c. 5% each year. Analysis relating spring (October) larval populations to % white clover measured in each plot in autumn (April) found the 2012 larval population to be statistically significantly larger in the ryegrass 6 kg/ha plots than 30 kg/ha plots. Thereafter, sowing rate had no significant effect on larval populations. From 2013 to 2015, spring larval populations had a negative relationship with the previous autumn % white clover with the relationship highly significant for the 2014 data. When CRW larval populations in spring 2013 to 2015 were predicted from the 2013 to 2015 autumn % white clover, respectively, based on their positive relationship in 2012, the predicted densities were substantially larger than those observed. Conversely, when 2015 spring larval data and % clover was regressed against 2012-2014 larval populations, observed densities tended to be higher than predicted, but the numbers came closer to predicted for the 2013 and 2014 populations. These differences are attributed to a CRW population decline that was not accounted by % white clover changes, the CR

Role of marker lesion when applying intravesical instillations of IL-2 for non-muscle-invasive bladder cancer comparison of the therapeutic effects in two pilot studies

Comparison of the therapeutic effect of treatment of non-muscle invasive bladder carcinoma (NMIBC) after intravesical Interleukin-2 (IL-2) instillations in the presence and absence of a marker tumour. Two pilot studies were performed in patients with NMIBC. The first study (10 patients) was performed in Krakow (Poland), the second (26 patients) in Vilnius (Lithuania). In Krakow the tumours were treated with incomplete transurethral resection (TUR) leaving a marker tumour of 0.5-1.0-cm followed by IL-2 instillations (3 × 10(6) IU IL-2) on five consecutive days. In Vilnius the tumours were treated with complete TUR, followed by IL-2 instillations (9 × 10(6) IU IL-2) on five consecutive days. During 30 months follow-up, the recurrence-free survival was 5/10 (50%) and 6/26 (23%) after incomplete and complete TUR, respectively. So, the ratio of the recurrence-free survival after incomplete/complete TUR of 50/23=2.2. The median of the recurrence-free survival is >20.5 months and 7 months after incomplete and complete TUR, respectively. So, this ratio was >20.5/7= >2.9. The hazard ratio which combines both the chance of the disease recurrence and its timing for both censored and uncensored cases was 0.53, again confirming the better outcome after incomplete TUR. A possible explanation for the better therapeutic effects after incomplete TUR compared with complete TUR is that the marker tumour has tumour-associated antigens (TAA) that could lead to an immune reaction that is stimulated by local application of IL-2. After complete TUR, no TAA are available to initiate and to stimulate an immune reaction; consequently, local IL-2 therapy is less effective after complete TUR. The results of these two pilot studies have led to the recent start of a randomised prospective clinical trial in which therapeutic effects of local IL-2 therapy after complete and incomplete TUR are compare

Rh-POP Pincer Xantphos Complexes for C-S and C-H Activation. Implications for Carbothiolation Catalysis

The neutral Rh­(I)–Xantphos complex [Rh­(κ³-_P,O,P-Xantphos)­Cl]_<i>n</i>, <b>4</b>, and cationic Rh­(III) [Rh­(κ³-_P,O,P-Xantphos)­(H)₂]­[BAr^F₄], <b>2a</b>, and [Rh­(κ³-_P,O,P-Xantphos-3,5-C₆H₃(CF₃)₂)­(H)₂]­[BAr^F₄], <b>2b</b>, are described [Ar^F = 3,5-(CF₃)₂C₆H₃; Xantphos = 4,5-bis­(diphenylphosphino)-9,9-dimethylxanthene; Xantphos-3,5-C₆H₃(CF₃)₂ = 9,9-dimethylxanthene-4,5-bis­(bis­(3,5-bis­(trifluoromethyl)­phenyl)­phosphine]. A solid-state structure of <b>2b</b> isolated from C₆H₅Cl solution shows a κ¹-chlorobenzene adduct, [Rh­(κ³-_P,O,P-Xantphos-3,5-C₆H₃(CF₃)₂)­(H)₂(κ¹-ClC₆H₅)]­[BAr^F₄], <b>3</b>. Addition of H₂ to <b>4</b> affords, crystallographically characterized, [Rh­(κ³-_P,O,P-Xantphos)­(H)₂Cl], <b>5</b>. Addition of diphenyl acetylene to <b>2a</b> results in the formation of the C–H activated metallacyclopentadiene [Rh­(κ³-_P,O,P-Xantphos)­(ClCH₂Cl)­(σ,σ-(C₆H₄)­C­(H)CPh)]­[BAr^F₄], <b>7</b>, a rare example of a crystallographically characterized Rh–dichloromethane complex, alongside the Rh­(I) complex <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(η²-PhCCPh)]­[BAr^F₄], <b>6</b>. Halide abstraction from [Rh­(κ³-_P,O,P-Xantphos)­Cl]_<i>n</i> in the presence of diphenylacetylene affords <b>6</b> as the only product, which in the solid state shows that the alkyne binds perpendicular to the κ³-POP Xantphos ligand plane. This complex acts as a latent source of the [Rh­(κ³-_P,O,P-Xantphos)]⁺ fragment and facilitates <i>ortho</i>-directed C–S activation in a number of 2-arylsulfides to give <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(σ,κ¹-Ar)­(SMe)]­[BAr^F₄] (Ar = C₆H₄COMe, <b>8</b>; C₆H₄(CO)­OMe, <b>9</b>; C₆H₄NO₂, <b>10</b>; C₆H₄CNCH₂CH₂O, <b>11</b>; C₆H₄C₅H₄N, <b>12</b>). Similar C–S bond cleavage is observed with allyl sulfide, to give <i>fac</i>-[Rh­(κ³-_P,O,P-Xantphos)­(η³-C₃H₅)­(SPh)]­[BAr^F₄], <b>13</b>. These products of C–S activation have been crystallographically characterized. For <b>8</b> in situ monitoring of the reaction by NMR spectroscopy reveals the initial formation of <i>fac</i>-κ³-<b>8</b>, which then proceeds to isomerize to the <i>mer</i>-isomer. With the <i>para</i>-ketone aryl sulfide, 4-SMeC ₆H₄COMe, C–H activation <i>ortho</i> to the ketone occurs to give <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(σ,κ¹-4-(COMe)­C₆H₃SMe)­(H)]­[BAr^F₄], <b>14</b>. The temporal evolution of carbothiolation catalysis using <i>mer</i>-κ³-<b>8</b>, and phenyl acetylene and 2-(methylthio)­acetophenone substrates shows initial fast catalysis and then a considerably slower evolution of the product. We suggest that the initially formed <i>fac</i>-isomer of the C–S activation product is considerably more active than the <i>mer</i>-isomer (i.e., <i>mer</i>-<b>8</b>), the latter of which is formed rapidly by isomerization, and this accounts for the observed difference in rates. A likely mechanism is proposed based upon these data

Local therapy of cancer with free IL-2

This is a position paper about the therapeutic effects of locally applied free IL-2 in the treatment of cancer. Local therapy: IL-2 therapy of cancer was originally introduced as a systemic therapy. This therapy led to about 20% objective responses. Systemic therapy however was very toxic due to the vascular leakage syndrome. Nevertheless, this treatment was a break-through in cancer immunotherapy and stimulated some interesting questions: Supposing that the mechanism of IL-2 treatment is both proliferation and tumoricidal activity of the tumor infiltrating cells, then locally applied IL-2 should result in a much higher local IL-2 concentration than systemic IL-2 application. Consequently a greater beneficial effect could be expected after local IL-2 application (peritumoral = juxtatumoral, intratumoral, intra-arterial, intracavitary, or intratracheal = inhalation). Free IL-2: Many groups have tried to prepare a more effective IL-2 formulation than free IL-2. Examples are slow release systems, insertion of the IL-2 gene into a tumor cell causing prolonged IL-2 release. However, logistically free IL-2 is much easier to apply; hence we concentrated in this review and in most of our experiments on the use of free IL-2. Local therapy with free IL-2 may be effective against transplanted tumors in experimental animals, and against various spontaneous carcinomas, sarcomas, and melanoma in veterinary and human cancer patients. It may induce rejection of very large, metastasized tumor loads, for instance advanced clinical tumors. The effects of even a single IL-2 application may be impressive. Not each tumor or tumor type is sensitive to local IL-2 application. For instance transplanted EL4 lymphoma or TLX9 lymphoma were not sensitive in our hands. Also the extent of sensitivity differs: In Bovine Ocular Squamous Cell Carcinoma (BOSCC) often a complete regression is obtained, whereas with the Bovine Vulval Papilloma and Carcinoma Complex (BVPCC) mainly stable disease is attained. Analysis of the results of local IL-2 therapy in 288 cases of cancer in human patients shows that there were 27% Complete Regressions (CR), 23% Partial Regressions (PR), 18% Stable Disease (SD), and 32% Progressive Disease (PD). In all tumors analyzed, local IL-2 therapy was more effective than systemic IL-2 treatment. Intratumoral IL-2 applications are more effective than peritumoral application or application at a distant site. Tumor regression induced by intratumoral IL-2 application may be a fast process (requiring about a week) in the case of a highly vascular tumor since IL-2 induces vascular leakage/edema and consequently massive tumor necrosis. The latter then stimulates an immune response. In less vascular tumors or less vascular tumor sites, regression may require 9–20 months; this regression is mainly caused by a cytotoxic leukocyte reaction. Hence the disadvantageous vascular leakage syndrome complicating systemic treatment is however advantageous in local treatment, since local edema may initiate tumor necrosis. Thus the therapeutic effect of local IL-2 treatment is not primarily based on tumor immunity, but tumor immunity seems to be useful as a secondary component of the IL-2 induced local processes. If local IL-2 is combined with surgery, radiotherapy or local chemotherapy the therapeutic effect is usually greater than with either therapy alone. Hence local free IL-2 application can be recommended as an addition to standard treatment protocols. Local treatment with free IL-2 is straightforward and can readily be applied even during surgical interventions. Local IL-2 treatment is usually without serious side effects and besides minor complaints it is generally well supported. Only small quantities of IL-2 are required. Hence the therapy is relatively cheap. A single IL-2 application of 4.5 million U IL-2 costs about 70 Euros. Thus combined local treatment may offer an alternative in those circumstances when more expensive forms of treatment are not available, for instance in resource poor countries